electromagnetism. electromagnetism canadas triumph accelerator putting it all together hydrogen...
TRANSCRIPT
Electromagnetism
Electromagnetism Canada’s Triumph Accelerator
Putting it All Together
Hydrogen Minus
Initial Acceleration
Electrostatic
Circular Motion
Magnetic Steering
Filtering
Electromagnetism Review
Magnetic Flux
We can describe the Density (or amount) of a Magnetic Field with the concept of Magnetic Flux.
Flux can be described as the total number of lines passing though an area, loop or coil.
It is a quantity of convenience used in Faraday’s Law.
Electromagnetism Review
cosB BA
Flux can be described as the total number of lines passing though an area, loop or coil.
Magnetic Flux
Magnetic Field(Tesla)
Area of Surface(m2)
Angle between field and normal line (B) on
the Surface Area
This can be described by the equation
Magnetic Flux
Electromagnetism Review Magnetic Flux Observations
The Stronger the Magnetic Field (B), the greater the Flux ().
The larger the Area (A), the greater the Flux ().
If the Magnetic Field (B) is perpendicular to the area, then the Flux () will be at a maximum.
cosB BA
Electromagnetism Review Magnetic Flux Units
Since B = BAcos(θ)
Flux has the units of B x A
This is (Tesla)(Metre2)
This is also called a Weber (Wb)
Electromagnetism Review Magnetic Flux Units
When the field is perpendicular to the plane of the loop
θ = 0 and ΦB = ΦB, max = BA
When the field is parallel to the plane of the loop.
θ = 90° and ΦB = 0The flux can be negative, for
example if θ = 180°
When the field is at an angle θ to the field B, ΦB is less than max.
Electromagnetism Review Magnetic Flux by Larger Area
You can increase the magnetic Flux by increasing the Surface Area
Electromagnetism Review Magnetic Flux by Strengthening the Field
You can increase the magnetic Flux by Strengthening the Field.
Electromagnetism Review Magnetic Flux Practice Question
cosB BA
You have a hula loop of radius 0.5m that is immersed in the Earth’s magnetic field (5x10-5 T). The hula loop is oriented in such a way that the normal is tilted at an angle of 200 away from the Earth’s North pole. What is the flux through the hoop?
cosB BA
5 25 10 0 cos.5 20B T m
2 cosB rB
53.7 10B Wb
Electromagnetism Review
Induction
Faraday’s Law describes the relationship between Electric Current and Magnetism.
Faraday’s Law
An Electric Current can induce a Magnetic Field, and a Magnetic Field can induce a Electric Current.
Just as Electricity needs to be moving to create a Magnetic field B, The Magnetic field B needs to be moving to create an Electric Current .
Electromagnetism Review
Law of Induction
Induced Voltage, V. A voltage is generated a Magnetic Force has been traditionally called an Electromotive Force or emf.
Faraday’s Law
Nt
Change in Magnetic Flux, Wb
Change in time, sThe number of coils of wire
•The greater the change in Magnetic Flux in a wire loop, the greater the Induced Current. •Less time corresponds to a greater Induced Current.•Adding more loops corresponds to a greater Induced Current.
Electromagnetism Review Faraday’s Law Practice Question
Nt
You have a coil of wire with 30 loops, each of which has an area of 2.0 x 10-3 m2. The Magnetic Field B is perpendicular to the surface. At time t=0 s, the Field B is measured at 1.0 T. At time, t=.2 s, the Field B is measured at 1.1 T. What is the average emf inside the coils.
Nt
3 21.1 1.0 2.0 10 cos 030
0.2 0.0
T T m
s s
cosBAN
t
0.03V
cosB BA
Electromagnetism Review
B Direction
Lenz’s Law describes the direction of the Electric Current produced by a changing Magnetic Field.
Lenz’s Law
The Thumb points in the direction of the Current. The fingers curl in the direction of the Magnetic Field.
Electromagnetism Review
B Direction
An influenced emf gives rise to a Electric Current whose Magnetic Field opposes the original change in Flux.
Lenz’s Law
The Right Hand Rule can aid us in these situations.
Electromagnetism Review Lenz’s Law
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Notice how the area is lessened when the loop is stretched.
Since the Flux is reduced, the Electric Current flows in the direction that would produce the B field. This direction tries to help maintain the original Flux.
Change in Flux
The induced current attempts to maintain the status quo.
Electromagnetism Review Lenz’s Law
Hoop Entering B Field
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When the loop enters a Magnetic Field. An Electric Current is induced (counter clockwise) in the loop as to oppose the increase in the Flux inside the loop.
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Electromagnetism Review Lenz’s Law
Hoop Inside B Field
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When the loop is total immersed inside a Magnetic Field there is No increase in Flux therefore there is No Current flow in the loop.
Electromagnetism Review Lenz’s Law
Hoop Exiting B Field
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When the loop exits a Magnetic Field. An Electric Current is induced (clockwise) in the loop as to oppose the decrease in the Flux inside the loop.
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Electromagnetism Review Lenz’s Law
Magnet Moving Through Hoop
When a magnet passes through a closed loop, the current will flow in what directions?
When a magnet enters the loop the current will flow clockwise (to oppose the increase in flux, make the end of the loop the magnet enters act like a North Pole) then zero. As the magnet exits, the current will then flow counter clockwise (to oppose the decrease in flux, ie look like a South Pole).
NS
When the North end of a magnet enters the loop from behind the screen, which direction, if any, will the current flow in the wire?
Electromagnetism Review Lenz’s Law
Magnet Moving Through Hoop
The current will flow clockwise to oppose the increasing flux.
Electromagnetism Review
EMF induced in a Moving Conductor
We have a conducting bar moving across a U shaped wire. The magnetic field is coming out of the screen. As the bar moves across the wire, the amount of Flux inside the loop increases.
EMF
Electromagnetism Review
EMF in a Moving Conductor
Induced Electromotive Force or emf.
Faraday’s Law
BLv
Velocity in m/s.
Length of moving conductor in m.
Magnetic Field in T.
Electromagnetism Review
EMF induced in a Moving Conductor
A 2.0 m rod is moving at 7 m/s perpendicular to a 1.2 T magnetic field heading into the screen. Determine the induced emf.
EMF
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Electromagnetism Review
EMF induced in a Moving Conductor
EMF
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BLv
1.2 2.0 7
17
mT m
s
V
+ vq
• Force on 1 moving charge:F = q v B sin(q)Out of the page (RHR)
• Force on many moving charges:F = (q/t)(vt)B sin(q)
= I L B sin(q) Out of the page!
v
L = vt
B
I = q/t+ + ++
distance
Electromagnetism Review
Force of Magnetic Field on Current
Recall
Torque on loop is t = L F sin(f) = ILWB sin(f)
Force on sections B-C and A-D: F = IBW
(length x width = area) LW = A
Torque is t = I A B sin(f)
W
L
a b
cd
B
I
XF
•F
Torque on Current Loop in B field
a b
cd
F
F
f
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Understanding: Torque on Current Loop
What is the torque on the loop below?
1) t < IAB
2) t = IAB
3) t > IAB
t = 0
Torque tries to line up the normal with B!(when normal lines up with B, f=0, so t=0! )
Even if the loop is not rectangular, as long as it is flat:
t = I A B sinf.
(area of loop)
Magnitude:
t = I A B sinf
Direction:
N
# of loops
a
b
c
dB
normal
f
F
F
Torque on Current Loop
between normal and B
B
Compare the torque on loop 1 and 2 which have identical area, and current.
I
Understanding: Torque
(1)
B
I
(2)
1) t1 > t2 2) t1 = t2 3) t1 < t2
Area points out of page for both!
f = 90 degrees
t = I A B sinf
Motional EMF
F = q v B sin(q)+ v
+-
-
+
Potential Difference F d/q
EMF = q v B sin(q) L/q
= v B L
B
L v
Velocity
Velocity
Moving + charge feels force downwards:
Moving + charge still feels force downwards: B
F
Angle between v and B
Understanding
Which bar has the larger motional emf? a b
v
v
ε = v B L sin(q)
q is angle between v and B
Case a: q = 0, so ε = 0
Case b: q = 90, so ε = v B L
“a is parallel, b is perpendicular”
Motional EMF circuit
Direction of Current
• Direction of force (F=ILB sin(q)) on bar due to magnetic field
I = e/R
• Magnitude of current
Clockwise (+ charges go down thru bar, up thru bulb)
To left, slows down
Moving bar acts like battery e = vBL
B
-+
V
What changes if B points into page?
= vBL/R
Motional EMF circuit
I = e/R = vBL/R
Still to left, slows down
Moving bar acts like battery e = vBL B
+ -
V
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Direction of Current
• Direction of force (F=ILB sin(q)) on bar due to magnetic field
• Magnitude of current
Counter-Clockwise (+ charges go up thru bar, down thru bulb)
Understanding
IncreaseStay the SameDecrease
Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure.
To keep the bar moving at the same speed, the force supplied by the hand will have to:
F=ILB sin(q))
B and v still perpendicular (q=90), so F=ILB just like before!
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Fm
o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o Fm
Understanding
True False
Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure.
To keep the bar moving to the right, the hand will have to supply a force in the opposite direction.
Current flows in the opposite direction, so force direction from the B field remains the same!
BLv
BLvI
R
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Fm
o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o Fm
Applications of Magnetic Force
Electric currents (in a wire, in a plasma, in a fluid solution, inside an atom) produce a disturbance in the surrounding space called the magnetic field. This magnetic field produces forces on any other macroscopic or microscopic currents.
Example: MRI: Magnetic field (several Tesla) from superconducting solenoid induces a net alignment of the microscopic currents inside each and every proton at the center of the Hydrogen atoms in your body.
Examples of Induced Current
Any change of current in primary induces a current in secondary.
Induced Current
The current in the primary polarizes the material of the core. The magnetic field of the primary solenoid is enhanced by the
magnetic field produced by these atomic currents. This magnetic field remains confined in the iron core, and only fans
out and loops back at the end of the core. Any change in the current in the primary (opening or closing
switch) produces a change in the magnetic flux through the secondary coil. This induces a current in the secondary.
TransformersA transformer is a device used to change the voltage in a
circuit. AC currents must be used.
75,000 V in the power lines
120 V in your house
s
p
s
p
p
s
N
N
V
V
I
I
p = primary
s = secondary
GeneratorA coil of wire turns in a magnetic field. The flux in the coil is constantly changing, generating an emf in the coil.
Applets
Wires:
Flux area:
Electric/Magnetic Balance:
Flux:
Induced Current:
Moving Bar:
Generator: